Site Section Links
KRONOS Vol IX, No. 1
THE CATASTROPHIC ROLE OF FLUID PRESSURE AND ELECTROMAGNETIC PHENOMENA IN THE MECHANICS OF OVERTHRUST FAULTING
MICHAEL M. HOBBY
An overthrust is the phenomenon of a slab of the Earth's crust having moved in a near-horizontal direction and having come to rest on an adjacent area. The movement itself is commonly referred to as a slide or a glide. It is distinguished from a flow, because the slab of crust has moved largely as a coherent unit, although parts of it may have been secondarily fractured and faulted or overturned in folds. Such folds are termed inversions. Within an inversion, material of a younger geologic age is found below older material. The plane over which the slab of crust is displaced is called a shearplane with respect to soil and rock mechanics, and is termed a low-angle reverse fault or sole fault with respect to structural geology. The thrust sole is the lowest thrust plane in an area of overthrusting, with layers above the sole commonly imbricated. Imbrication is frequently observed in association with instantaneous displacement, and plastic deformation is frequently associated with creep. The overthrust phenomenon becomes more enigmatic with this observation.
Traditionally, geologists tried to interpret the phenomenon of overthrust faulting in terms of gravity sliding. However, in many cases the angle of the shearplane is too low (nearly parallel to the horizontal) to explain satisfactorily movements of the magnitude observed, even when a tectonic shock is assumed to have provided the triggering effect. For near-horizontal soil movements of much smaller dimensions, Terzaghi (1943) had already pointed to the possible importance of high water-pressure in subsoil horizons; Hubbert and Rubey (1959) probably were the first to apply this concept to the mechanics of overthrust faulting.
[*!* Image] Figure 1. Schematic diagram of large-scale thrust sheet, modeled by C. K. Longwell after examples in California and southern Nevada. Reprinted by permission.
The general problem in finding an explanation has been how to support the assertion that the shear strength of soil and rock may become so low that near-horizontal displacement may occur. According to Coulomb's equation, the shear strength, S, is expressed as
S = c + n tan f
in which c is cohesion, n is the pressure normal (perpendicular) to the plane, and phi is the angle of internal friction. It is not difficult to conceptualize the reduction of cohesion to a near-zero value. This can be easily explained by assuming a shock, e.g., of a tectonic nature. However, reducing the quantity n tan f to a point sufficiently low to allow the friction to be overcome has been for all a difficult problem.
The concept of stress can be understood by imagining that any volume within the crust is a cube small enough that stresses acting upon that cube are uniform across each of its faces, with the force per unit area being resolved into two components, one normal to the face (s) and one parallel to it (t) which acts as a shear stress. Since t may be further resolved into two components perpendicular to each other and to s, we may superimpose the configuration upon a set of coordinate axes.
[*!* Image] Figure 2. Reprinted by permission.
When all six faces of the cube are considered, a total of 18 components of stress result.
[*!* Image] Figure 3. Reprinted by permission.
However, if the cube is not in motion, either by translation or rotation, then 12 of the 18 stresses are in equilibrium, leaving only six components, one for each face of the cube, and normal to it. This representation of stresses can then be further simplified by reducing the size of the cube to a point, at which time the opposing vectors are added, yielding three resultant stresses, mutually perpendicular, and passing through the point. Having previously identified s as the normal stress, we can represent these three stress directions as the principal directions of stress, with the greatest called s1, the intermediate one called s2 and the least principal stress called s3 All three may be equal, as in hydrostatic stress, or any two might be equal, as in confining pressure, but commonly they are thought of as non-equivalent, and are thus represented as a stress ellipsoid.
[*!* Image] Figure 4. The stress ellipsoid, with principle axes [s]1 [s]2 [s]3. Reprinted by permission.
Rock failure occurs when the stress applied exceeds the structural integrity of the rock. Research in rock mechanics has thoroughly established that such faults (produced during failure) occur at an angle of 0-45 degrees from s1, the greatest principal direction of stress, but are commonly oriented at about 30 degrees to s1. In the case of normal faults, s1, is vertical, because the acceleration of gravity acting upon the mass of the crust is usually the greatest principal direction of stress. A block view of a normal fault might look similar to Figure 5.
[*!* Image] Figure 5. Types of fault. From Earth by Frank Press and Raymond Siever. Copyright (c) 1978 by W. H. Freeman and Company. All rights reserved.
Reverse faults may also occur when s1, is vertical, as shown in Figure 5. It can be observed that these faults are both at about 60 degrees from the horizontal (90 - 30 = 60). In the case of overthrusts, however, the low-angle reverse faults are from 0-45 degrees (commonly close to 30 degrees ) from the horizontal, indicating that s1, was parallel to the horizontal when the thrusting occurred (refer to Figure 1).
[*!* Image] Figure 6a.
Figure 6b. Geological map and cross-section of the Arltunga Metamorphic Complex in Central Australia, where pervasive thrusts in the basement and metamorphic rock may duplicate the sequence as much as ten times. Reprinted by permission.
[*!* Image] Figure 7. Unconformities, folds, and thrust sheets in a section of the southern Alps. [After Structural Geology by L. U. De Sitter. McGraw-Hill Book Company. Copyright (c) 1964.
Folds and faults in a section of the Juras, an example of a folded mountain belt. According to one hypothesis, the beds overlying the Triassic were sheared off and deformed independently of the older rocks below.
From Earth by Frank Press and Raymond Siever. Copyright (c) 1978 by W. H. Freeman and Company. All rights reserved.
THE HUBBERT-RUBEY HYPOTHESIS
Prior to Hubbert and Rubey's hypothesis asserting the role of fluid pressure in the mechanics of overthrust faulting ( 1959), no plausible mechanism was known which might account for the enigma. Lowangle thrusts of Paleozoic or Mesozoic crust sheets have attained displacements of 500 km. Dimensions may range from 0.5-2.0 km in thickness, and to hundreds of kilometers in length. Hubbert and Rubey suggested that abnormal fluid pressures might approach overburden pressures sufficiently close to allow overthrust by the equation
tcrit = s tan f = (1-l) S tan f
where a is the normal stress across the plane of slippage, tcrit is the shear strength of the material when s is zero, and phi is the angle of internal friction, with l equal to the ratio of fluid pressure to overburden pressure (normal stress S in the equivalent expression at the end of the equation). They also hypothesized gravitational sliding down a near-zero angle of slope by the equation
tan q =(1-l) tan f
which results in the slope down which a plate must slide approaching zero as increasing fluid pressure changes the quantity (l) to unity. The resulting state of incipient flotation renders the concept of overthrust plausible. Numerous writers objected to the hypothesis, or felt its general application to all overthrusts was invalid; Laubscher (1960), Birch (1961), Raleigh and Griggs (1963), Davis (1965), and Hsü (1969). Birch felt that the quantity to must be retained, resulting in
t = to + (1-l) S tan f
Hubbert and Rubey responded (1961) to Birch's objection by arguing against the retention of to once sliding had been initiated:
Raleigh and Griggs expanded the fluid pressure hypothesis to include the effect of the toe in overthrusting:
Davis objected to the general application of Hubbert and Rubey's model, arguing that the syncline-generated theory could not apply to all overthrusts, since they occurred in metamorphic rocks and various geologic environments not subject to the application of their theory.
In response to Davis, Hubbert and Rubey admitted the unproven aspect of their theory, but urged its continued application as a working hypothesis:
Hsü argued that to for sedimentary rocks (generally about 200 bars) had to be overcome during overthrust faulting if gravitational sliding was to be considered valid as an hypothesis. He maintained that the cohesive strength of thrust blocks could not be disregarded. He associated the Heart Mountain thrust not with cohesively bound blocks, but with landslides (such as the Flims, Goldau, and Vaiont slides) which moved at speeds of many meters per second. He further proposed that imbrication would occur at the front of overthrust blocks sliding downslope under their own weight due to the effect of the toe. He felt that when movement was governed by frictional sliding, it would be catastrophic, and that, if it was accomplished by creep, to could not be omitted. Like Hsü, Braddock (1978) wrote:
Laubscher insisted that Archimedes' principle could not be made a part of the mechanism:
Speaking of the Jura thrust, Heard and Rubey quoted Laubscher's calculation (1961, p. 246) of the maximum permissible shear stress of the material at the thrust sole to be no greater than 30-90 bars. They also noted that the measured (non-geologic) shear stress "in the anhydrite plus water paste ranges from 50 bars for the fast tests (3 x 10-7/sup> sec.)to 35 bars for the slow tests (3 x 10-4/sup> sec.)". Although Heard and Rubey emphasized that under geologic conditions (constant stress over a long time interval) stress would be further reduced, this seems unnecessary to establish plausibility.
Fertl (1976) reported that shales acting as semi-permeable membranes have generated osmotic pressures in sandwiched permeable sandstones of up to 400 atmospheres:
[*!* Image] Figure 8. Diagram of osmotic flow – fresh water toward saline water (after Jones, 1969). Reprinted by permission.
Figure 9. Theoretical values of osmotic pressure across a clay membrane (after Jones, 1969). Reprinted by permission.
Obviously, such awesome pressures need only to be triggered to produce potentially catastrophic phenomena.
The Hubbert-Rubey model has remained viable even with the difficulties inherent in its general application, and in spite of the ascendancy of the plate tectonics hypothesis. The phenomena associated with the dehydration of gypsum (Heard and Rubey, 1966) strengthened the plausibility that fluid pressures along essentially planar, horizontal surfaces could develop even in sediments which contain little or no water. Hubbert and Rubey restricted themselves entirely to the fluid pressure mechanism, which produced a plausible but still limited explanation.
When we examine the forces involved at any given point, all vectorial forces must be addressed, regardless of their origin. The limited applicability of the Hubbert-Rubey hypothesis resulted from the exclusion of vectors normal to the Earth from consideration. For instance, overburden pressure may be simply resolved into the components m and g, where m is the mass of the overlying sediments per unit area and g is the acceleration of gravity acting upon that mass. The product mg is the overburden pressure, exclusive of the vertical component of any stresses originating within the sedimentary or other rocks themselves. Since mg as a vectorial quantity is normal to the surface of the Earth, it is generally counter to the oppositely-directed vectorial quantity, pp (pore fluid pressure).
In Figure 10, at a selected point along the thrust sole, fluid pressure pp is directed against mg. It is important to note this fact, since it is essential to further analysis of the free-body diagram presented.
[*!* Image] Figure 10. Labels: Overlying Sediment. Slightly Inclined Thrust Sole. Random Point Along Thrust Sole. pp (pore pressure).
For reference, let us imagine that our random point is within the wellbore at a drilling site. The weight of the drilling mud constitutes the source of vector mg(bar), and the formation (fluid) pressure constitutes the source of vector pp. Every geologist knows that if the mud-weight falls below that necessary to contain the formation pressure, a kick results. The power of a kick can be catastrophic (at least to a drilling crew) even when expelled through a wellbore only a few inches in diameter. It must be obvious to all that regional pressures exist at depth. This point is essential to the Hubbert-Rubey hypothesis.
VELIKOVSKY AND OVERTHRUSTS
In view of these observations, what are the implications of the thesis of Velikovsky (1950) upon the phenomenon of overthrust faulting? To date, no geologist has addressed this profoundly significant question; yet Velikovsky's theory of objects of planetary mass and cometary behavior making close approaches to the Earth clearly has direct application to the to near-zero across a region, we might legitimately expect incipient flotation and/or crustal perforation to result. But how might this occur?
While Velikovsky's thesis did propose that objects of planetary mass and cometary behavior made close approaches to the Earth, neither I nor any other geologist is presently competent to prove the reality of such events. It must also be acknowledged that arguments whose only thrust is to assert that such events could not occur are not germane, since they are relevant only to individual predisposition, competent scientists being aligned on both sides of the question. What does have scientific merit is the consideration of what results might be observed if such approaches were to occur.
[*!* Image] Figure 11.
In Figure 11, two masses of planetary magnitude are portrayed. Each mass is surrounded by an infinite number of vectors directed toward its center, each of which has a value which is the product mg(bar) for that particular vector. However, sediment thicknesses, density, and distribution with respect to the center of mass vary from vector to vector. Gravity anomalies reflect this fact across the surface of the Earth. Therefore, mg(bar) is not a constant from point to point around the globe. Similarly, the triaxiality of the Earth also distorts the value from place to place. We might expect, therefore, to encounter a wide range of values for mg(bar). But at no point would we expect to encounter a zero or near-zero value under normal conditions. The quantity mg(bar) is thus s1, over most of the Earth most of the time.
If an event such as that portrayed in Figure 11 were to occur, however, although the mass at any given point would remain constant, the value of g(bar) would oscillate dramatically. Let us consider two opposite points, one located on each of the two masses. Each has a vector associated with it. For the point on m(l), the vector would be m(l)(bar)g,, and for the point on m(2), the vector would be m(2)g(bar)(2) . Prior to the near approach pictured in Figure 11, each vector constitutes the overburden pressure on all points between it and the center of mass of the object with which it is associated, and it has a constant value which is the product mg(bar). However, any two spherically distributed masses, in this case m, and m(2), are related by the equation
This is Newton's law of gravitational attraction between two spherically distributed masses. F is the force exerted upon each by the other. As a vectorial quantity, it is always equal in magnitude and opposite in direction for the two masses, regardless of the difference in their masses. The distance between the centers of mass of the two objects is r. Therefore, when r^2 becomes sufficiently small, the gravitational attraction between the two bodies becomes large. Consequently, the force F becomes increasingly larger the closer the approach of the two bodies. And Facts against the quantity mg(bar) at any point between the two masses. As the two approach, the vectorial quantities m(1)g(bar)(1), and m(2) g(bar)(2) are reduced in value by the counter-action of F acting against them (oppositely directed). Now let us return to Figure 10 and observe what is happening to the two values, pp and mg(bar). Since the value of m is constant, the only quantity that can change (in the Earthward-directed vector) is g(bar), which becomes smaller as the other planetary mass approaches. The effect is less dramatic if the force F is not normal to a point, and the greater the angle of declination from normal, the less the reduction in the value of g. If the angle exceeds 90 degrees, an increase in the value of g would in fact result.
Additionally, not only will the overburden pressure mg(bar) decrease, but the value of pp may actually increase simultaneously! This assertion seems at first glance to be mechanically impossible and to violate Boyle's law (PV=constant) when applied to fluids, since body tides resulting from a critical decrease in the value of mg(bar) would increase pore volume within the sediments accordingly. However, recent space investigations have established that many bodies within our solar system are electrically charged. When two such bodies attain a near-approach, electromagnetic forces generate significant electric currents, and these currents produce heat. As observed by Boyle in his gas studies, the introduction of heat to a pressure volume system alters its parameters. This would be particularly true above 218 atmospheres (the critical pressure of water) where the undefined phase behaves more like a gas than a liquid. Therefore, even with the increasing pore volume produced by body tides in the Earth, pore pressure might still be augmented further.
Catastrophic body tides in the Earth could result even in the absence of this non-Newtonian mechanism, because the two bodies move relative to one another; the points where the described changes in the values of mg(bar) and pp occur will shift accordingly along the surface of the Earth, producing undulations, or body tides. Actually, body tides with an amplitude of roughly 50 cm occur routinely on the Earth due to lunar movements, but they pass unnoticed because we undergo the same motion. Such tides might not pass unnoticed if a planetary mass larger than the Moon approached the Earth closely, because a close approach engenders a horizontal disequilibrium as well (the horizontal component of g(bar) on all points not normal to it) which could be the source of the push imagined by Hubbert and Rubey.
This push would be increased by the action of the magnetic couple acting on a body with an unequal distribution of mass. If the approach was close enough, this couple acting alone could conceivably produce the horizontal disequilibrium requisite for overthrusts on an essentially horizontal thrust sole. In concert with the horizontal component of g(bar), the horizontal stress could indeed become s1 for a time. Conversely, it is not requisite that the event would pull the Earth apart and destroy it unless the approach exceeded the crustal integrity of the planet. In the case of an overthrust, we may be witnessing the results when such magnitudes are almost attained. The arc configuration of some thrusts is also suggestive of this type of event. The Velikovsky thesis provides a mechanism which can account for all types of overthrusts known to us to date, and it circumvents many of the difficulties of the Hubbert-Rubey hypothesis acting alone. Geologists would rather appeal to forces below than to forces originating above, but the phenomenon of overthrust is so unique that it would be fatuous not to investigate all possibilities.
By considering these possibilities within the confines of the Hubbert-Rubey hypothesis, we see immediately that crustal displacements of a regional character become increasingly plausible, particularly in those areas where tectonism has been active, for it is in these areas that the requisite compressional forces tend to be greatest. The obvious restriction of overthrusts to such areas may be viewed as evidence in support of this conclusion. Velikovsky has provided the clue to the trigger mechanism which might be applied either to initiate or produce such displacements entirely by overthrust, since on a stress diagram, there is no denying the fact that s3 could become vertical and s1 horizontal, the conditions we know to be requisite for low-angle reverse faults.
Author observing a small thrust (s1 horizontal) on the south flank of the Cerro de Cristo Rey pluton in Chihuahua, Mexico. Note that in this case, the horizontal "push " was provided by a pluton pushing up through the crust at the surface. The strata first folded, then thrusted. This particular thrust is displaced only .4 meters, thereby relieving the internal stress in the rock.
Additional Figure Credits: Figure 1: From Earth by Frank Press and Raymond Siever (W. H. Freeman and Company, 1978), by courtesy of John Haller.
Figures 2, 3, 4, and 6: From An Outline of Structural Geology by Bruce E. Hobbs, Winthrop D. Means and Paul F. Williams. Copyright (c) 1976 by John Wiley and Sons, Inc. All rights reserved.
Figures 8 and 9. From Abnormal Formation Pressures (Development in Petroleum Science, 2) by Walter H. Fertl. Copyright (c) 1976 by Elsevier Scientific Publishing Co. All rights reserved.